[PAST EVENT] Colloquium: Rational Processes -- Beyond Markov Chains

Peter Buchholz, Department of Computer Science, TU Dortmund, will introduce Rational Processes and show that, when compared to Markov Processes, they define a modeling approach to handle large state spaces in an efficient way.

Markov processes (MPs) in discrete or continuous time are an established model type for system analysis and optimization in various areas including computer science, logistics or systems biology. MPs have an intuitive probabilistic interpretation and can also be interpreted in terms of vectors of matrices observing specific properties. If one skips the probabilistic interpretation at a detailed level and considers only conditions on vectors and matrices, a more general class of processes can be defined. These processes have been described recently, are denoted as Rational Processes (RPs) and have their roots in Matrix Exponential Distributions and Rational Arrival Processes which are natural extensions of Phase Type Distributions and Markovian Arrival Processes. The advantage of RPs compared to MPs is an increased modeling power for a fixed number of states, and the possibility to use several tools from linear systems theory to compute minimal representations. This implies that for every RP and every MP and up to similarity transformations unique minimal RP representation exists and this representation can be computed. Such a result is not available in the class of MPs.

In the talk RPs are introduced, modeling formalisms like Stochastic Petri Nets, Queueing Networks or Stochastic Automata Networks are slightly extended to describe RPs and numerical methods for the analysis of RPs are briefly presented. It is shown that RPs can be used like MPs in many situations as an appropriate tool for system analysis. In particular compositional methods for system analysis that are available for MPs can be extended to RPs and define a modeling approach to handle large state spaces in an efficient way. The talk ends with an outline of open questions and current research activities in the area.

Bio: Peter Buchholz holds a diploma degree (1987), a doctoral degree (1991) and a habilitation degree (1996) all from the University of Dortmund in Germany, where he has been at the computer science faculty in several positions until 1999. Afterwards he joined the department of computer science at Dresden University of Technology as an associate professor for modeling and simulation. In 2003 he returned to the TU Dortmund becoming a full professor for practical computer science. His research interests include techniques and tools for model based system analysis and their application to computer systems, computer networks, logistics networks and related systems. One particular research area for more than 20 years are techniques for model building and analysis of Markov chains. He has developed various approaches to model systems in a structured and hierarchical way, map this structure on the underlying Markov chain and exploit structure for a more efficient analysis of processes with huge state spaces.